A taxi journey takes the passenger to a destination 8 km south and 3 kn west of its starting point. Find the distance and bearing of the destination from its starting point.

Using trigonometry.

An inverse variatiοn includes the pοints (8, 3) and (2, n), the value οf n is 12.

Inverse variatiοn fοrmula refers tο the relatiοnship οf twο variables in which a variable increases in its value, the οther variable decreases and vice-versa. In οther wοrds, the inverse variatiοn is the mathematical expressiοn οf the relatiοnship between twο variables whοse prοduct is a cοnstant.

Using the given pοints, we can set up a prοpοrtiοn tο find k:

8 * 3 = k

2 * n = k

Setting the twο expressiοns fοr k equal tο each οther, we get:

8 * 3 = 2 * n

24 = 2n

Dividing bοth sides by 2, we get:

n = 12

Therefοre, the value οf n is 12.

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the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

Corresponding angles are angles that are in the same position at each intersection where a straight line crosses two others. In the given list of angles, we can see that:

Angles 1 and 3 are corresponding angles, because they are on opposite sides of the line and are in the same position relative to the other lines.

Angles 5 and 7 are corresponding angles, for the same reason.

Angles 6 and 8 are corresponding angles, because they are alternate interior angles (they are on opposite sides of the transversal and inside the two lines).

Angles 7 and 2 are vertical angles, not corresponding angles.

Angles 6 and 3 are alternate interior angles, not corresponding angles.

Angles 1 and 6 are alternate interior angles, not corresponding angles.

Therefore, the corresponding angles are A. 7 and 2, C. 5 and 7, and E. 6 and 8. The correct answer is A, C, and E.

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However, it can improve one's problem-solving skills and logical reasoning abilities, which could indirectly lead to improvements in various aspects of life, including interpersonal relationships.

I would decide my endless goal by carefully considering my values, desires, and potential paths towards achieving them.

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Answer: six minutes

Step-by-step explanation: 8 / 4 = 2 , 3 x 2 = 6

Answer:

108

Step-by-step explanation:

Let's assume that there are "x" scouts attending the jamboree.

The number of tins of soup required to feed x scouts would be x/2.

The number of tins of frankfurters required to feed x scouts would be x/3.

The number of tins of fruit required to feed x scouts would be x/4.

Therefore, the total number of tins required to feed x scouts would be:

x/2 + x/3 + x/4 = (6x + 4x + 3x) / 12 = 13x/12

Since we know that 117 tins were opened, we can set up the equation:

13x/12 = 117

Solving for x, we get:

x = 108

Therefore, there were 108 scouts attending the jamboree.

Step-by-step explanation:

Question 1

This question has two parts. First, answer Part A. Then, answer Part B.

Part A

Fill in the blank question.

There are many cylinders with a height of 18 meters. Let r represent the radius in meters and V represent the volume in cubic meters.

Complete the equation that represents the volume V as a function of the radius r.

V =

πr2

Complete the table.

r V

1

π

2

π

4

π

Part B

Select the correct choices to complete the sentence.

Complete the statement about the radius and volume of a cylinder.

If the radius of a cylinder is doubled, the volume 1 of 2.

Select Choice

.

Complete the statement about the graph of this function.

The graph of this function 2 of 2.

Select Choice

a line.

Answer:

5(d) = miles student A ran

8(d-3) = miles student B ran

Step-by-step explanation:

when d = days passed

5(d) = miles student A ran

8(d-3) = miles student B ran

The total area of the composite figure is 200 square feet.

We can view the figure as a triangle and a rectangle.

The dimensions of the rectangle are 24ft by 6ft,so its area is:

A = 24ft*6ft = 144ft²

Now for the triangle, remember that the area of a triangle of base B and height H is:

a = B*H/2

In this case we can see that the base is:

B = 24ft - 8ft - 8ft = 8ft

And the height is:

H = 20ft - 6ft = 14ft

Then the area of the triangle is:

a = 8ft*14ft/2 = 56 ft²

The total area is:

Area = 56 ft² + 144ft² = 200 ft²

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Answer:

fourth option

Step-by-step explanation:

sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]

and

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]

Quadrilateral A: Parallelοgram, Rectangle, Rhοmbus, Square.

Quadrilateral B: Trapezοid, Isοsceles Trapezοid

Quadrilateral C: Kite, Trapezοid

Square and Rectangle:

Bοth have fοur right angles, but the square has fοur cοngruent sides, while the rectangle dοes nοt necessarily have cοngruent sides. Therefοre, a square is a rectangle, but nοt all rectangles are squares.

Rhοmbus and Square:

Bοth have all sides cοngruent, but the square alsο has fοur right angles, while the rhοmbus dοes nοt necessarily have right angles. Therefοre, a square is a rhοmbus, but nοt all rhοmbuses are squares.

Parallelοgram and Rhοmbus:

Bοth have οppοsite sides parallel, but the rhοmbus alsο has all sides cοngruent, while the parallelοgram dοes nοt necessarily have cοngruent sides. Therefοre, a rhοmbus is a parallelοgram, but nοt all parallelοgrams are rhοmbuses.

Trapezοid and Kite:

Bοth have twο pairs οf adjacent sides that are cοngruent, but the kite alsο has οne pair οf οppοsite cοngruent sides, while the trapezοid dοes nοt. Therefοre, a kite is a type οf trapezοid, but nοt all trapezοids are kites.

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The solution to the equation x² + 3x = 0 when solved for variable x are x = -3 and 0

Equations are statements with equal values

Given the following equation

x² + 3x = 0

Factor out x from the equation

So, the equation becomes

x(x + 3) = 0

The above equation means that

x = 0

Also, it means that

x + 3 = 0

When the equation is evaluated, we have

x = 0 and x = -3

Now that we have the values of x, we can conclude that the solutions are x = 0 and x = -3

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Answer:

  A, D, E

Step-by-step explanation:

You want to know the properties applicable to a square among those listed.

Quadrilaterals can be classified according to the relationships between their sides. These relationships also give rise to relationships between the diagonals.

The diagonals have the same midpoint in a parallelogram.

The diagonals are the same length in a parallelogram that is a rectangle.

A square is a rectangle that has adjacent sides of the same length (A). That means its diagonals have the same midpoint (E), and they are the same length (D).

__

Additional comment

When segments have the same slope, they are parallel. Consecutive sides intersect, so cannot have the same slope (E). Likewise, the diagonals intersect, so cannot have the same slope (C).

The 6 m/s, and 5 m/s speeds of the sprinters, the 150 meters length of the race, and the 10 meters head start of sprinter B indicates that the three statements are true, and the correct option is therefore;

True, True, True

The speed of an object is the ratio of the distance traveled by the object to the duration of the motion.

The distance sprinters are to run = 150 meters

The speed of sprinter A = 6 m/s

Speed of sprinter B = 5 m/s

The head start of sprinter B = 10 meters

Statement A; Sprinter A is leading the race at the 12 seconds mark

At the 12 seconds mark, we get;

The distance covered by sprinter A = 6 m/s × 12 s = 72 m

The distance covered by sprinter B = 10 m + 5 m/s × 12 s = 70 m

Therefore, sprinter A is leading sprinter B at the 12 seconds mark

Statement A is True

Statement B; Sprinter A will win the race

The time it takes sprinter A to run the race = 150 m/(6 m/s) = 25 s

Sprinter B takes (150 m - 10 m)/(5 m/s) = 28 s to finish the race

Sprinter A therefore, finishes before sprinter B, and sprinter A wins the race

Statement B is; True

Statement C; The graphs of the two functions intersect before the race ends

The location of sprinter B ahead of A at the start of the race and A ahead of B at the 12 seconds mark, indicates that the sprinter A passes sprinter B along the race and the graphs intersect before the race ends. The statement is therefore; True

The possible options, obtained from a similar question posted on the internet are;

True, True, True

False, True, True

True, False, True

True, True, False

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The total price of the ring after increment is $15900

A percentage is a term used in mathematics to describe a value or ratio that may be expressed as a fraction of 100. If we need to calculate a percentage of a number, we should first divide it by 100 before multiplying it by the remainder. As a result, the proportion denotes a component per 100. Percent is what the word "percent" means. Its symbol is the letter "%".

The current price of the ring= $ 15,000

Increase in percentage=6

New price:

15000*(1+0.06)=15900

The total price of the ring after increment is $15900

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The most individuals with a certain trait that follow a normal distribution would appear in the middle range.

If you graph the numbers of individuals with a certain trait that follow a normal distribution, the most individuals will appear in the middle range of the graph.

When graphing a normal distribution, it creates a bell-shaped curve.

The curve is symmetric and highest at the center, which indicates that the most individuals fall under the middle range of the graph.

The shape of the curve represents the frequency distribution of the data.

The horizontal axis is marked off in intervals of standard deviations from the mean.

The vertical axis shows the frequency, or the number of times each score occurs in the data set.

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Yes it's rhombus ......... .......

The surface area οf the square pyramid is 144 square units.

A square pyramid has a square base, sο tο find the surface area, we need tο find the area οf the square base and the area οf each οf the fοur triangular faces, and then add them tοgether.

The area οf the square base is: 8 x 8 = 64 square units

Tο find the area οf each οf the fοur triangular faces, we need tο find the area οf each triangle and then add them tοgether. Each triangle has a base οf 8 and a height οf 5 (the slant height οf the pyramid).

The area οf each triangle is:

(1/2) x base x height = (1/2) x 8 x 5 = 20 square units

Since there are fοur triangular faces, the tοtal area οf the triangular faces is: 4 x 20 = 80 square units

Finally, we can find the tοtal surface area by adding the area οf the square base and the area οf the fοur triangular faces:

64 + 80 = 144 square units

Therefοre, the surface area οf the square pyramid is 144 square units.

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Given:-

To find:-

Answer:-

Here we can assume the shape of the cup to be cylindrical . And the volume of a cylinder is given by;

[tex]\implies V = \pi r^2 h \\[/tex]

where ,

Assuimg that the cups differ only in height and not in width (diameter) , we can say that ;

[tex]\implies V \propto h \\[/tex]

So , we can write;

[tex]\implies \dfrac{V_s}{V_l}=\dfrac{h_s}{h_l}\\[/tex]

[tex]\implies \dfrac{V_s}{18\ oz}=\dfrac{6\ in.}{8 \ in.}\\[/tex]

[tex]\implies V_s = \dfrac{6(18)}{8} \\[/tex]

[tex]\implies \underline{\underline{ V_s =13.5 \ oz}} \\[/tex]

Hence the volume of the smaller cup is 13.5 oz .

and we are done!

The second term of the finding sequence is 25.

When you are confronted by a question like this, you can make a simple equation, combine like terms, isolate the variable, and solve.

"5 consecutive odd numbers" basically means x + (x + 2) + (x + 4) + (x + 6) + (x + 8). Each time you add 2 more to ensure there are no even numbers. Otherwise, it wouldn't be only consecutive odd numbers.

We are told the sum of these numbers is 135. This means x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

This might seem a bit intimidating, but there are actually only a couple of steps.

Combine like terms.

In this case, the like terms are the 5 times x appears and the numbers 0, 2, 4, 6, and 8.

x + x + x + x + x = 5 • x, or 5x.

0 + 2 + 4 + 6 + 8 = 20

So by combining like terms, we can simplify (x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135 down to just 5x + 20 = 135.

Isolate the variable.

Now we just have to isolate x. The value of x is the lowest term in the sequence.

5x + 20 = 135

To isolate x, first subtract 20 from both sides. Then, divide both sides by 5.

5x + 20 - 20 = 5x

135 - 20 = 115

5x = 115

5x / 5 = x

115 / 5 = 23

x = 23

The lowest term in the sequence is 23.

Identify all numbers in the sequence.

Now that we know x, we can find the rest of the numbers in the sequence by plugging the lowest value into the original equation we created.

(x + 0) + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 135

(23 + 0) + (23 + 2) + (23 + 4) + (23 + 6) + (23 + 8) = 135

23 + 0 = 23 This is the first and lowest term in the sequence.

23 + 2 = 25 This is the second term in the sequence.

23 + 4 = 27 This is the third term in the sequence.

23 + 6 = 29 This is the fourth term in the sequence.

23 + 8 = 31 This is the fifth and last term in the sequence.

Now we know the sequence is 23, 25, 27, 29, 31.

Finding the Answer:

To find the answer, locate the second term in this sequence.

23, 25, 27, 29, 31

The second term is 25.

The complete question is-

The sum of 5 consecutive odd numbers is 135. What is the second number in this sequence?

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The coordinates of the fourth vertex of the parallelogram are given as follows:

To find the coordinates of the fourth vertex of the parallelogram, we must consider the fact that opposite sides of a parallelogram are parallel and equal in length.

Considering the side formed by the vertices (-1,9) and (4,7), the difference of the coordinates is given as follows:

Hence, compared to the vertex (0,-2), the coordinates of the remaining vertex are given as follows:

Then the coordinates of the fourth vertex are given as follows:

(-5,0).

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Answer:

Let x be the number of hot dogs sold.

Then the number of sodas sold is 3x.

The total number of sodas and hot dogs sold is 132, so we can write:

x + 3x = 132

4x = 132

x = 33

Therefore, the number of hot dogs sold is 33, and the number of sodas sold is 3x = 3(33) = 99.

Step-by-step explanation:

Answer:

There are 4 queens in a pack of 52 cards, and there are also 13 diamonds and 26 black cards (13 clubs and 13 spades).

To find the probability of getting a queen or a diamond or a black card, we need to add the probabilities of each event happening and subtract the probability of getting a card that is both a queen and a diamond (the queen of diamonds).

Probability of getting a queen = 4/52 = 1/13

Probability of getting a diamond = 13/52 = 1/4

Probability of getting a black card = 26/52 = 1/2

Probability of getting the queen of diamonds = 1/52

So, the probability of getting a queen or a diamond or a black card is:

(1/13) + (1/4) + (1/2) - (1/52) = 51/52 or approximately 0.98

Therefore, the probability of getting a queen or a diamond or a black card is approximately 0.98.

According to the question the value of ST is 3 + 4x.

Value is the worth or importance that is placed on something. It can refer to tangible items such as money, goods, or services, or intangible concepts such as a person's beliefs, attitude, or sense of self-worth. Values are essential for guiding decisions and behaviour. They provide a framework for understanding what is important to an individual or a society, and can inform how people interact with their environment.

Given equation : 4x + 3 = ST
To find the value of ST, we need to subtract 4x from both sides of the equation.
4x + 3 - 4x = ST - 4x
3 = ST - 4x
Now, add 4x to both sides of the equation.
3 + 4x = ST
Therefore, the value of ST is 3 + 4x.

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Answer:

54

Step-by-step explanation:

So a right angle has one right angle and each angle is equal to ninety degrees. So you have 90+36=126. Sum of angles in a triangle is 180 so subtract 126 from it to get 54.

Have a wonderful day and feel free to ask me again. Peace

The line segment that shows the base that corresponds to the given height of the triangle is; Line segment A

We are given the parameter being that a height is labeled as seen on the triangle in attached figure.

Now, what we want to achieve is to find the specific segment which tells us the specific base that corresponds to the given specific height of the triangle

We know that the base of the triangle is that particular side of the triangle on which the height is perpendicular.

In the given attached figure, it is clear that the Height is perpendicular to side A.

Therefore, side A will represent the base of triangle.

Finally, line segment A tells us the base that corresponds to the given height of the triangle.

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Answer:

w=20cm

Step-by-step explanation:

Tough question.  

We are not told whether the surface area is only what can be seem from the top, or does it include regions beneath the butterfly.  I made the assumption it is from the top

I had to make an assumption that since the butterfies are similar, they wll have the same ratio of width and height.  We will assume an "effective height,"  a value of height that when multiplied by the width will yield the correct surface area of 53 cm^2.

See the attached worksheet.

The effective height for the smaller butterfly is 13.25cm.  This multiplied by the given width (4cm) produces the surface area of 53 cm^3.  The ratio of width to height (w/h) is 0.302.

We've already made the assumption that the width to height of the larger butterfly will be the same.  Now we can use the larger area (1325 cm^2) with the width to height ratio as follows:

 Area = w*h

Since w/h is = 0.302, we can write w = 0.302h or h = (w/0.302)

 1325 cm^2 = w*h

1325 cm^2 = w*(w/0.302)

w^2 = 200

w = 20 cm

(I made several assumptions in this analysis.  Review them carefully).

We can say that after answering the offered question Therefore, the equation exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]{-\frac{4\sqrt{261}}{65}}[/tex]

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

[tex]$\sec A = \frac{1}{\cos A}$ to find the cosine of angle $A$.[/tex]

[tex]$\sec A = -\frac{65}{7}$, we have $\frac{1}{\cos A} = -\frac{65}{7}$.\\$$\cos A \cdot \frac{1}{\cos A} = \cos A \cdot \left(-\frac{65}{7}\right)$$\\$$[/tex]

Since angle A is in Quadrant III, we know that [tex]$\cos A < 0$ and $\sin A < 0$.[/tex]

Using the Pythagorean identity[tex]$\sin^2 A + \cos^2 A = 1$, we can solve for $\sin A$:[/tex]

[tex]$$\sin^2 A + \left(-\frac{7}{65}\right)^2 = 1$$\\$$\sin^2 A + \frac{49}{4225} = 1$$\\$$\sin^2 A = \frac{4176}{4225}$$\\$$\sin A = -\frac{4\sqrt{261}}{65}$$[/tex]

Therefore, the exact value of[tex]$\sin A$ i[/tex]n simplest radical form using a rational denominator is [tex]${-\frac{4\sqrt{261}}{65}}$[/tex]

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75% of the time, a dart will fall inside a square rather than on the circular dartboard.

The ratio of the area of the circle to the square is 16/64 = 1/4. So, the area outside the circle but inside the square is 3/4 of the total area of the square. The probability of landing the dart in this region is 3/4.

To find the percentage, we can multiply by 100:

3/4 × 100 = 75%

Therefore, to the nearest percent, the probability that the dart lands inside the square but not on the circular dartboard is 75%.

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Answer: x=3

              y=9

Step-by-step explanation: im about 75.94 percent sure about this, i hope it helps